where is initial water saturation which maybe equal to critical or less than critical like for example in petroleogenetic rocks.
The model assumes no gas presence in pores.
The alternative form of the Oil+Water RPM Corey @model can be presented as a function of normalized water saturation :
s = \frac{s_w - s_{wi}}{1-s_{wi}-s_{orw}} |
which changes between for initial water saturation and for maximum water saturation .
In this case equations and take form:
OIL | WATER |
---|
k_{row}(s_o) = k_{rowc} \cdot (1-s)^{n_{ow}} |
| k_{rwo}(s_w) = k^*_{rwoc} \cdot (s - s^*)^{n_{wo}} |
|
| s^* = \frac{s_{wco}-s_{wi}}{1-s_{wi}-s_{orw}} |
|
k^*_{rwoc} = k_{rwoc} \cdot \left( \frac{1-s_{wi}-s_{orw}}{1-s_{wco}-s_{orw}} \right)^{n_{wo}} |
|
and fractional flow function is going to be:
f_w = \frac{M_{rwo}}{M_{rwo} + M_{row}} = \frac{(s-s^*)^{n_{wo}}}{(s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}}} |
|
\dot f_w = \frac{d f_w}{ds} = g \cdot (s-s^*)^{n_{wo}-1} \cdot
\frac{\n_{wo} (1-s)^{n_{ow}} + n_{ow} (s-s^*) (1-s)^{n_{ow}-1}
}
{\left[ (s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}} \right]^2}
|
|
where
g = \frac{M_{rowc}}{M_{rwoc}} \cdot \left( \frac{1-s_{wco}-s_{orw}}{1-s_{wi}-s_{orw}} \right)^{n_{wo}} |
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Relative Permeability / RPM @model
[ Permeability ] [ Absolute permeability ]